Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Labeling techniques and typed fixed-point operators
Higher order operational techniques in semantics
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Unification in Lambda-Calculi with if-then-else
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Automated Reasoning in Higher-order Logic: Set Comprehension and Extensionality in Church's Type Theory
Progress in the Development of Automated Theorem Proving for Higher-Order Logic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Terminating Tableaux for the Basic Fragment of Simple Type Theory
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
The 5th IJCAR automated theorem proving system competition - CASC-J5
AI Communications
Analytic tableaux for higher-order logic with choice
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Satallax: an automatic higher-order prover
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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While many higher-order interactive theorem provers include a choice operator, higher-order automated theorem provers so far have not. In order to support automated reasoning in the presence of a choice operator, we present a cut-free ground tableau calculus for Church's simple type theory with choice. The tableau calculus is designed with automated search in mind. In particular, the rules only operate on the top level structure of formulas. Additionally, we restrict the instantiation terms for quantifiers to a universe that depends on the current branch. At base types the universe of instantiations is finite. Both of these restrictions are intended to minimize the number of rules a corresponding search procedure is obligated to consider. We prove completeness of the tableau calculus relative to Henkin models.